Clustering-based classification method of loading schemes of multi-span beams under multiple patch loading

  Objectives  It is of great significance to classify a large number of loading schemes quickly and accurately, and obtain loading schemes with similar structural design requirements or decide the structural design of multi-span beams.

  Methods  In this paper, a classification method for the loading schemes of multi-span beams under multiple patch loading is proposed. For the given multi-span beams and vehicles, the worst-case analysis of multi-span beams under multiple patch loading is used to obtain the maximum bending moment, maximum shear force and maximum deflection of a multi-span beam under all possible loading schemes; then the XB index and fuzzy C-means (FCM) algorithm are used to classify the loading schemes according to the above results. For three-span beams and four-span beams, the influence of the ratio of span and moment of inertia on the classification results is analyzed.

  Results  The numerical results show that the classification of multi-span beams with different structural forms is not exactly the same. The maximum margin of error between the results of multi-span beam structures with variable span ratio or variable moment of inertia ratio calculated with the classification of equal span rigidity multi-span beams and actual worst-case results is less than 2%.

  Conclusions  The relationships between the loading schemes of multi-span beams under multiple patch loading is analyzed, providing a reference for the design of deck structures under multiple patch loading.